Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#19081 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
880 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,26)(22,30)(23,24)(28,29)(31,32)(33,34)(36,37,42,39)(38,46,49,51)(40,45,41,44)(43,50,47,48);(20,21)(22,27)(23,28)(24,26)(25,29)(30,34)(31,33)(32,35)(36,38)(37,43)(39,47)(40,48)(41,50)(42,49)(44,46)(45,51);(20,22,25,32)(21,27,29,35)(23,30,24,31)(26,33,28,34)(36,39,42,37)(38,47,49,43)(40,44,41,45)(46,50,51,48);(20,23,25,24)(21,28,29,26)(22,31,32,30)(27,33,35,34)(36,40,42,41)(37,44,39,45)(38,48,49,50)(43,46,47,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12069);